Transreal Arithmetic and Analysis

Two papers have been released. The first paper, Perspex Machine VIII: Axioms of Transreal Arithmetic describes how to divide by zero consistently in a non-trivial way. This shows that division by zero is no longer an error. Amongst other things, the paper explains why the standard model of arithmetic is not valid. The second paper, Perspex Machine IX: Transreal Analysis explains how to extend calculus so that it works with transreal numbers. This paper disposes of various counter "proofs" that attempt to show that division by zero is impossible. The paper ends with a very simple equation demonstrating the possibility of division by zero and challenges the reader to accept it.